Imagine yourself sitting in a boat, traveling over water with velocity u on a windless day. A small flag is attached to the boat's mast: in what direction will it point?

Seen from the boat, the flag always points to the rear, because in the boat's frame of reference, a wind with velocity –u seems to be blowing. It always points in the same direction.

What if the day is not windless? If a wind is blowing with velocity v? In the frame of the boat, the air now moves with velocity v – u , a vector sum, with the direction of v specified relative to the boat ("in the boat's frame"). The flag now points neither downwind, nor to the rear, but somewhere in between.

Suppose the boat now changes direction. In the frame of the boat u is still directed to the rear, but the wind now seems to come from a different direction, relative to the boat. Consequently, the direction of v changes, and the flag, pointing alongthe new v – u, has a different direction as well. For more about this effect, see here

Apparent Displacement of Stars

This section is about starlight, not about boats and flags. From Newton's days, astronomers have tried to find how far the stars were by the parallax method, using the diameter of the Earth's orbit as a baseline. They carefully measured the positions of stars at times half a year apart--representing two positions of the Earth separated by 300,000,000 km--and then checked whether the positions of stars in the sky changed. They soon found that, indeed, the positions did change. The trouble was that the observations did not make much sense.

Jean Picard, one of the early French astronomers, made possible precise observations by introducing crosshairs in the telescope eyepiece. With this instrument he noted around 1680 that the observed positions of stars were not always the same. John Flamsteed, the astronomer royal of Britain--head of the Royal Observatory in Greenwich--confirmed those shifts. For instance Polaris, the pole star, seemed to travel annually around an ellipse whose width was 40", 40 seconds of arc.

As discussed in the section on parallax, that might suggest that the distance to Polaris was 1/40 of a parsec or less than 0.1 light year. However, the shifts in position did not occur at the times they were expected . The greatest shift of Polaris in any given direction occured not when the Earth's was at the opposite end of its orbit, as it should have been, but 3 months later.

For instance, in the drawing above, the apparent position of Polaris should have been shifted the furthest in the direction of "December" when Earth was in its "June" position, which is as far as it can go in the opposite direction. Instead, it happened in September, when the Earth had moved 90° from its position in June. In hindsight, the important quantity was not the displacement of Earth, but its velocity, which in September pointed towards the direction towards which Polaris was displaced.